Genericity of Fr\'echet smooth spaces

If a separable Banach space contains an isometric copy of every separable reflexive Fr\'echet smooth Banach space, then it contains an isometric copy of every separable Banach space. The same conclusion holds if we consider separable Banach spaces with Fr\'echet smooth dual space. This improves a result of G. Godefroy and N. J. Kalton.Comment: 34 page

Operators between subspaces and quotients of L1

We provide an unified approach of results of L. Dor on the complementation of the range, and of D. Alspach on the nearness from isometries, of small into isomorphisms of L1. We introduce the notion of small subspace of L1 and show lifting theorems for operators between quotients of L1 by small subspaces. We construct a subspace of L1 which shows that extension of isometries from subspaces of L1 to the whole space are no longer true for isomorphisms, and that nearly isometric isomorphisms from subspaces of L1 into L1 need not be near from any isometry.Comment: 35 page

Strong proximinality and polyhedral spaces

In any dual space X, the set QP of quasi-polyhedral points is contained in the set SSD of points of strong subdifferentiability of the norm which is itself contained in the set NA of norm attaining functionals. We show that NA and SSD coincide if and only if every proximinal hyperplane of X is strongly proximinal, and that if QP and NA coincide then every finite codimensional proximinal subspace of X is strongly proximinal. Natural examples and applications are provided

Strong subdifferentiability of norms and geometry of Banach spaces

summary:The strong subdifferentiability of norms (i.e\. one-sided differentiability uniform in directions) is studied in connection with some structural properties of Banach spaces. It is shown that every separable Banach space with nonseparable dual admits a norm that is nowhere strongly subdifferentiable except at the origin. On the other hand, every Banach space with a strongly subdifferentiable norm is Asplund

Renormings and extremal structures

In this paper we use renorming techniques to settle several questions on extremal structures of Banach spaces. We construct a unitary vector in a dual space which is not a weak∧ -unitary. We construct an exposed point in the unit ball of a Banach space X that remains exposed in the unit ball of X(4) but is not extreme in the unit ball of X(6)

The Effects of Stacking on the Configurations and Elasticity of Single Stranded Nucleic Acids

Stacking interactions in single stranded nucleic acids give rise to configurations of an annealed rod-coil multiblock copolymer. Theoretical analysis identifies the resulting signatures for long homopolynucleotides: A non monotonous dependence of size on temperature, corresponding effects on cyclization and a plateau in the extension force law. Explicit numerical results for poly(dA) and poly(rU) are presented.Comment: 4 pages and 2 figures. Accepted in Phys. Rev. E Rapid Com

On peak phenomena for non-commutative H∞H^\infty

A non-commutative extension of Amar and Lederer's peak set result is given. As its simple applications it is shown that any non-commutative $H^\infty$-algebra $H^\infty(M,\tau)$ has unique predual,and moreover some restriction in some of the results of Blecher and Labuschagne are removed, making them hold in full generality.Comment: final version (the presentation of some part is revised and one reference added

Renormings and extremal structures

Abstract. In this paper we use renorming techniques to settle several questions on extremal structures of Banach spaces. We construct a unitary vector in a dual space which is not a weak * -unitary. We construct an exposed point in the unit ball of a Banach space X that remains exposed in the unit ball of X (4) but is not extreme in the unit ball of X (6)

Completeness in the Mackey topology

Bonet and Cascales [Non-complete Mackey topologies on Banach spaces, Bulletin of the Australian Mathematical Society, 81, 3 (2010), 409-413], answering a question of M. Kunze and W. Arendt, gave an example of a norming norm-closed subspace N of the dual of a Banach space X such that mu(X, N) is not complete,where mu(X, N) denotes the Mackey topology associated with the dual pair aEuroX, NaEuro parts per thousand. We prove in this note that we can decide on the completeness or incompleteness of topologies of this form in a quite general context, thus providing large classes of counterexamples to the aforesaid question. Moreover, our examples use subspaces N of X* that contain a predual P of X (if exists), showing that the phenomenon of noncompleteness that Kunze and Arendt were looking for is not only relatively common but illustrated by "well-located" subspaces of the dual. We discuss also the situation for a typical Banach space without a predual-the space c (0)-and for the James space J.The first author is supported in part by MICINN and FEDER (project no. MTM2008-05396), by Fundacion Seneca (project no. 08848/PI/08), by Generalitat Valenciana (GV/2010/036), and by Universitat Politecnica de Valencia (project no. PAID-06-09-2829). The second author is supported in part by MICINN project no. MTM2011-22417, by Generalitat Valenciana (GV/2010/036), and by Universidad Politecnica de Valencia (project no. PAID-06-09-2829).Guirao Sánchez, AJ.; Montesinos Santalucia, V. (2015). Completeness in the Mackey topology. Functional Analysis and Its Applications. 49(2):97-105. https://doi.org/10.1007/s10688-015-0091-2S97105492J. Bonet and B. Cascales, “Non-complete Mackey topologies on Banach spaces,” Bull. Aust. Math. Soc., 81:3 (2010), 409–413.M. Fabian, P. Habala, P. Hájek, V. Montesinos, and V. Zizler, Banach Space Theory. The Basis for Linear and Nonlinear Analysis, CMS Books in Math., Springer-Verlag, New York, 2011.P. Pérez-Carreras and J. Bonet, Barreled Locally Convex Spaces, North-Holland Mathematical Studies, vol. 131, North-Holland, Amsterdam, 1987.P. Civin and B. Yood, “Quasi-reflexive spaces,” Proc. Amer. Math. Soc., 8:5 (1957), 906–911.J. Diestel, Sequences and Series in Banach Spaces, Graduate Text in Math., vol. 92, Springer-Verlag, New York, 1984.K. Floret, Weakly Compact Sets, Lecture Notes in Math., vol. 801, Springer-Verlag, Berlin, 1980.G. Godefroy, “Boundaries of convex sets and interpolation sets,” Math. Ann., 277:2 (1987), 173–184.R. C. James, “On nonreflexive Banach space isometric with its second conjugate,” Proc. Nat. Acad. Sci. USA, 37 (1951), 174–177.G. Köthe, Topological Vector Spaces I, Springer-Verlag, New York, 1969